# Are QM and SR completely compatible?

1. Aug 14, 2004

### Gonzolo

Hi, correct me if I'm wrong, but quantum mechanics and special relativity seem to fit pretty well together. With Klein-Gordon's equation and Dirac's equation anyway, they seem to be able to live with each other quite happily. Are there cases in which they can't? Is this what Q Field theory deals with? What are the main problems or obstacles in this area, if any? I'm talking about Special R. only here, NOT General Relativity.

2. Aug 14, 2004

### jcsd

Obviously adding special relativty doesn't make it easier, but AFAIK there aren't any fundamental problems in QFT with marrying SR and quantum physics.

Of course there are features of the Schroedinger equation (one f the most obvious being that time and space have different orders in it) that make it non-relativtsic, but as you've pointed out there are several relatvistic wave equations anyhap.

3. Aug 15, 2004

### NEOclassic

The SR incremental mass not convertable to photo energy

Regardless of whether in Classic Mechanical or Quantum mechanical situation,
only the rest mass of the high speed particle is available for Einstein's E=mc^2 conversion; consider the following axiom:

Axiom: An intrinsic property of matter is that its mass, to the extent that the part that is the result of Einstein/Lorentz velocity-dependent mass-enhancement, can only be converted back to energy in the manner of classical physics. I.e., E = mc^2 applies uniquely to the rest mass of the high velocity material particle – before the rest mass of a particle that is mass-enhanced (by the rule of Special Relativity) becomes available for photo conversion it, along with its excess mass, behaves according the traditional conservation laws of kinetic energy and momentum.

Corollary: logically (contrapositive-wise) any loss of a moving particle’s mass (on the occasion of its impact with matter) that is manifest by an increase in heat, momentum or kinetic energy of that matter is necessarily achieved at the expense of the particle’s total mass that existed as the result of Special Relativity.

For example, when a cosmic-ray proton is cracked in two by impact each pion's mass is decreased from 469 MeV to 139.6 MeV as the kinetic etc energy of the meson increases by 330 MeV; after about 0.03 microseconds it unwinds to become a muon of mass, 105.7 MeV that finishes unwinding and moving while losing another 33 or so MeV (in about 2 microseconds) of its mass leaving only the electrons and positrons that can only be destroyed by annihilatin. possible remnants are +muon > e+e-e+ and -muon > e-e+e-.

Ipse Dixit, Neoclassic cheers, Jim

4. Aug 17, 2004

### eljose79

uumm..perhapas i don,t agree with Dirac,s equation it implies the existence of a metric gab whereas in quantum mechanics there is no metric or gab so i think Dirac,s equation is only an approximation to quantizying special relativity...

5. Aug 18, 2004

### humanino

Dirac's equation is perfectly fine and well suited. We know that for a while now. I am absolutly positive eljose79 : SR and QM have been unified, that is the original motivation for QFT, which has been around for a while now.

6. Aug 18, 2004

### Tom Mattson

Staff Emeritus
No, it assumes the existence of the metric gab. The Dirac equation starts with the assumption that SR is correct.

There is in relativistic quantum mechanics. Or do you think that Schrodinger's QM is the "real" QM and that Dirac's is not?

It's the exact quantization of dynamical variables for spin-1/2 particles that is consistent with SR.